Tags » 3-manifolds

Not all finitely-presented groups are fundamental groups of closed 3-manifolds

In our previous note Amalgamated products and HNN extensions (IV): Markov properties, we saw that for every and for every finitely-presented group , there exists a -dimensional closed manifold whose fundamental group is . 1,254 more words


MOO is classical

The simplest quantum 3-manifold invariant is the Murakami-Ohtsuki-Okada (MOO) invariant. It comes from Chern-Simons theory in the way that the Reshetikhin-Turaev invariant comes from Chern-Simons Theory. 1,270 more words


SnapPy 2.3 released

Marc Culler and I are pleased to announce version 2.3 of SnapPy. New features include:


Mr Spock complexes (after Aitchison)

The recent passing of Leonard Nimoy prompts me to recall a lesser-known connection between the great man and the theory of (cusped) hyperbolic 3-manifolds, observed by my friend and former mentor Iain Aitchison. 993 more words

Hyperbolic Geometry

Taut foliations and positive forms

This week I visited Washington University in St. Louis to give a colloquium, and caught up with a couple of my old foliations friends, namely Rachel Roberts and Larry Conlon. 1,878 more words


Understanding the anomaly

I’ve recently been looking at the following paper in which -TQFT anomalies are treated carefully and various old constructions of Turaev and Walker are elucidated: 1,082 more words